KA-0132Eliminate impossible choices by bounding
4 points, difficulty 2 of 3Level 3–4about 90sAna has exactly 5 coins, each worth either 2 cents or 5 cents. Which of these could NOT be her total?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
List every total from 0 fives up to 5 fives.
2The strategy
With exactly five coins, the only thing that varies is how many are fives. Run that from zero to five and write down each total - six totals in all, and everything else is impossible.
3The full solution
The totals are 10, 13, 16, 19, 22 and 25. Each extra five adds 3. There is no 21 in the list.
Solution
The reliable way
With exactly five coins, the only choice is how many are 5-cent coins. With none, the total is 10. Each time a 2 is swapped for a 5 the total rises by 3, so the possible totals are 10, 13, 16, 19, 22 and 25. Every offered value appears except 21, so 21 is impossible. The transferable idea: when one quantity controls everything, run it through its whole range and read the possibilities off - the answer to a could-not question is whatever the list misses.
The elegant way
Every total is 10 plus a multiple of 3, and 21 - 10 = 11 is not a multiple of 3.
Why this is on the test: Could-not questions need the full set of possibilities, and building the list is faster and safer than testing the odd one out.